Stepanov-like pseudo almost automorphic mild solutions to nonautonomous evolution equations

Pseudo Asymptotic Behavior of Mild Solution for Nonautonomous Integrodifferential Equations with Nondense Domain

“…Proof. First, we show that (1) admits a unique bounded solution given by (31), which is similar to the proof of [26,Theorem 3.3]. For ∈ (R, , ), it is clear that ℎ(⋅) := (⋅, (⋅), ( )(⋅)) ∈ (R, , ) by Lemma 23 and Corollary 19; then ‖ℎ‖ < ∞.…”

“…see[26]). A mild solution of (1) is a continuous function : R → satisfying ( ) = ( , ) ( ) + ∫ ( , ) ( , ( ) , ( ) ( ))(16) for all ≥ , , ∈ R. Assume that ℎ ∈ E(R, , ) and ( 1 ), ( 2 ), and (…”

Weighted pseudo asymptotically periodic mild solutions of evolution equations

“…Remark 4.8 (A 1 ) is usually called "Acquistapace-Terreni" conditions, which was first introduced in [1] and widely used to study nonautonomous differential equations in [1,16,17,22]. If (A 1 ) holds, there exists a unique evolution family (U (t, s)) t≥s on X, which governs the homogeneous version of (4.8).…”

Pseudo almost periodic and automorphic mild solutions to nonautonomous neutral partial evolution equations

“…In this work, we use the new approach of weighted almost periodic functions developed recently in [8]. In particular, in [33] Zhanrong Hu and Zhen Jin, proved the new existence and uniqueness theorems of pseudo almost automorphic mild solutions to the equation (1.1). For contributions on nonautonomous evolution equations in Banach spaces, see [23,26,32].…”

“…In this paper, motivated by [8,9,32,33], we use the measure theory to de ne an Stepanov-ergodic function and we investigated many interesting properties of such functions, we study the completeness and the composition theorem of the functional space of µ-pseudo almost automorphic functions and µ-pseudo almost periodic functions in the sense of Stepanov.…”